The hyperbolic geometry of the universe and the wedding of general relativity theory to quantum theory

The equation of the radius of the universe, which I found as a solution to the first dynamical equation of cosmology (time-time component), reveals that the curvature of the universe must be negative, yielding a hyperbolic and open universe. Moreover, when I applied this equation to the Planck scale, it predicted the Planck length, which verifies my solution. Such a solution is well satisfied when applied to the second dynamical equation of cosmology (space-space component). Moreover, the solution predicted the equation of state The negative pressure implies an accelerated expansion of the universe in agreement with current observations.